What is 0.9ln(6)-2.4ln(8) ?

The solution to 0.9ln(6)-2.4ln(8) is ln(0.03411…)

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simplify 0.9ln(6)-2.4ln(8)

simplify

0.9 ln (6) - 2.4 ln (8)

ln (0.03411 \dots)

Decimal Notation

- 3.37807 \dots

Solution steps

0.9 ln (6) - 2.4 ln (8)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

0.9 ln (6) = ln (6^{0.9})

= ln (6^{0.9}) - 2.4 ln (8)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2.4 ln (8) = ln (8^{2.4})

= ln (6^{0.9}) - ln (8^{2.4})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (6^{0.9}) - ln (8^{2.4}) = ln (\frac{6 ^{0.9}}{8 ^{2.4}})

= ln (\frac{6 ^{0.9}}{8 ^{2.4}})

\frac{6 ^{0.9}}{8 ^{2.4}} = 0.03411 \dots

= ln (0.03411 \dots)

ln (2 x^{\frac{8}{1 - x}})

- lo g_{10} (1.5 \cdot 1 0^{- 5})

- lo g_{10} (1.41 \cdot 1 0^{- 6})

\frac{1}{3} (4 ln^{2} (2) + ln^{2} (3))

ln (\frac{∣ x + 1 ∣}{∣ x - 1 ∣})